Prediction of some turbulent flows using upwind and hybrid discretısa tion schemes and the two-eouation turbulence model

Abstract

The paper presents the use of a numerical solution procedure for the prediction of steady, in­ compressible and two-dimensional turbulent flow in a pipe, in sudden expansions in pipes, and over a back­ ward-facing step using upwind and hybrid discretisation schemes. The numerical procedure employs a two-equation turbulence model, which entails the solution of two differential equations of transport for characteristics of turbulence; nameIy, the kinetic energy of tur­bulence and its rate of dissipation. The Reynolds stresses are related to the mean velocity gradients through a scalar turbulent viscosity, calculated from the above turbulence variables. In the near-wall regions, wall functions are employed. The predictions results from simultaneous solution of differential equations for conservation of mass and momentum, together with equations describing the transport of turbulence, by means of a finite-difference solution procedure. The predictions obtained using upwind and hybrid discretisation schemes are compared with each other and with published experimental data. For flows in which recirculation is present, the use of hybrid scheme results in closer agreement with measurements. In general, the predictions made are in good qualitative agreement with experiment.